The head of the Prison Service today admitted that hundreds of inmates abscond every year from open prisons across the country.

The admission came as the Home Office faced fresh embarrassment over the revelation that the prison and probation services lose track of four prisoners a day. Figures obtained from the Liberal Democrats showed that more than 13,000 prisoners have escaped, absconded or disappeared while on temporary release in the last 10 years.

Nick Clegg, Lib Dem home affairs spokesman, said the figures were another serious blow to the public's faith in the criminal justice system.

He said they suggested that prisoners are being "re-categorised early in order to free up cells.

"Overcrowding elsewhere in the prison system can be no excuse for placing dangerous or untrustworthy prisoners in open conditions, where they may pose a threat to the public," Mr Clegg said.

Speaking earlier after it emerged that almost 400 prisoners had walked out of Leyhill open prison in Gloucestershire during the past seven years, Phil Wheatley, director general of the Prison Service, said the figure was "broadly consistent" with others. Mr Wheatley said that the "vast majority" were rearrested promptly but indicated that up to a quarter were not and some would go on to reoffend.

"Some will have reoffended so I am not minimising the risk that there is when a prisoner absconds," he said, adding that running open prisons carried "a degree of risk".

Prison Service figures show that offenders have been disappearing from Leyhill open prison at the rate of more than one a week. Robbery and burglary offenders were the main absconders from but 22 murderers and seven rapists have escaped since 1999.

Leyhill is one of 13 open prisons in England. The figures showed that 393 prisoners absconded from Leyhill between 1999 and 2006. The Home Office last night refused to reveal absconding rates for the other open prisons.

"The absconds from Leyhill last year, which is just over 60, is broadly consistent with other open prisons. Leyhill is about in the middle of the range," Mr Wheatley said.

Asked if the most serious offenders had been returned to prison, he told BBC Radio 4's The World At One he could not talk about individual cases.

The Leyhill figures were obtained by David Laws, the Lib Dem MP for Yeovil, after local police told him there had been mini waves of crime in the area carried out by criminals on the run. Mr Laws said the figures were another example of the "shambolic state" of the Home Office.

"Murderers, rapists, burglars, robbers are escaping from this one prison at the rate of almost two a week. Serious criminals who should be locked up are getting out to commit extra crimes," Mr Laws told the Daily Telegraph.

A Home Office spokesman said that open prisons like Leyhill played an important role in the resettlement of offenders as they approached the end of their sentences.

The disclosures about Leyhill are the latest in the series of damaging revelations for the Home Office in recent weeks.

Yesterday the department refused to apologise for wrongly labelling 2,700 innocent people as criminals because of errors made by the bureau that identifies whether people have convictions.

The errors by the Criminal Records Bureau led to ordinary people - from court ushers to students - being wrongly identified as pornographers, thieves and violent robbers. In some cases, people were turned down for jobs or university places while others had had to be fingerprinted at their local police station to prove that they were not criminals.

In a separate issue, the shadow home secretary, David Davis, has tabled a series of questions about allegations that an immigration official offered to help an asylum seeker stay in Britain in return for sex.

According to the Observer, an employee at the Immigrations and Nationality Directorate (IND) offered to coach an 18-year-old Zimbabwean woman - who had previously been the victim of rape - for her asylum interview in return for sex.

Only last March, an internal inquiry cleared staff at Lunar House of claims they offered female applicants visas in return for sex, although it found that there had been "isolated incidents of unprofessional behaviour".

The disclosures came as ministers and officials continued to grapple with the fallout from the foreign prisoners deportation fiasco, which has been going on for weeks.

To add to their difficulties it was disclosed that 232 foreign nationals arrested in counter-terrorism operations had been allowed to remain in Britain as asylum seekers, including 18 who had only applied for refugee status following their arrest.

The Home Office is also continuing to investigate claims that five illegal immigrants arrested after being sent to work at the IND's central London offices had been employed on the service's premises for years.

It is all likely to ensure that the new home secretary, John Reid, will face a rough ride when he appears this week before the Commons home affairs committee for the first time.